Question 190: AC fundamentals

Question

A 10 $$\Omega$$ resistance is connected across 220V $$-$$ 50 Hz AC supply. The time taken by the current to change from its maximum value to the rms value is :

Accepted Answer

$$\Rightarrow$$ i = i
0
sin$$\omega$$t
when i = i
0
i
0
= i
0
sin$$\omega$$t
1
$$\Rightarrow$$ $$\omega$$t
1
= $${\pi  \over 2}$$ ..... (i)
When i = $${{{i_1}} \over {\sqrt 2 }}$$
$${{{i_1}} \over {\sqrt 2 }}$$ = i
0
sin$$\omega$$t
2
$$\Rightarrow$$ $$\omega$$t
2
= $${\pi  \over 4}$$ ...... (ii)
Time taken by current from maximum value to rms value
$$ \Rightarrow ({t_1} - {t_2}) = {\pi  \over {2\omega }} - {\pi  \over {4\omega }} = {\pi  \over {4\omega }} = {\pi  \over {4 	imes 2\pi f}}$$
$$ = {1 \over {8 	imes 50}}$$
$${1 \over {400}}$$ sec
= 2.5 ms

Answer

2.5 ms

Answer

1.5 ms

Answer

3.0 ms

Answer

4.5 ms

AC fundamentals

A 10 $\Omega resistance is connected across 220V -$ 50 Hz AC supply. The time taken by the current to change from its maximum value to the rms value is :

Choose the correct answer: